Graphene is a very interesting form of carbon. It represents a two dimensional crystal which contains electron gas with interesting properties. Interaction of ion beam with 2D materials has been studied both experimentally (see for example [1,2]) and theoreticaly ([3,4]). The results of simulations currently do not agree with experiments and there is therefore a space for improving the calculations.
When protons pass through graphene foil they can be neutralized or H- ion can be formed. The goal...

doc. RNDr. Martin Čížek, Ph.D.

Ústav teoretické fyziky (116. • 32-UTF)

3

Zsolt Bačo

Quantization of dynamics of molecular rattleback.

Rattleback is a small boat-shaped toy, that is placed on table and spun. If the direction of the spin is "incorrect" the boat starts to vibrate and the direction of the spinning is gradually inverted (see "rattleback" on wikipedia and the videos shown there). Apparent violation of angular momentum conservation is consequence of interaction with the table. The goal of this thesis is to design a molecular system attached to surface with similar behavior

doc. RNDr. Martin Čížek, Ph.D.

Ústav teoretické fyziky (116. • 32-UTF)

3

Graduates

Name

bachelor thesis

supervisor

department

graduated

Lukáš Timko timkolukas(at)seznam.cz

Gravitational lensing by combined continuous and discrete matter

Gravitational lenses are typically modeled either by a continuous mass distribution (in the case of strong and weak lensing by galaxies or galaxy clusters), or by a set of discrete point masses (in the case of microlensing by stars or stellar systems). However, continuously modeled astrophysical systems do have their discrete component: lensing galaxy clusters contain individual galaxies; lensing galaxies contain dwarf galaxies, globular clusters, and at a finer scale individual stars. The objective of the work is to test the influence of an added discrete component on the lensing of continuously modeled objects using simple models, and to assess potential implications for the analyses of observed lenses.

Mgr. David Heyrovský, Ph.D.

Ústav teoretické fyziky (116. • 32-UTF)

2017

Ondřej Basler

Numerical determination of the scattering length for atomic collisions

Numerical determination of the scattering length for low-energy collisions of atoms, which is needed e.g. when modelling the Bose-Einstein condensate.

RNDr. Karel Houfek, Ph.D.

Ústav teoretické fyziky (116. • 32-UTF)

2017

Hedvika Gedeonová

Time-dependent solution of the generalized Fano model

Variety of physical processes in quantum mechanics can be described as interaction of the so called discrete state with continuum. Resonant scattering can serve as a most typical example. Here, the metastable state, which is described by a square integrable wave function, corresponding to capture of the particle near the target, decays into the continuum of scattering states. When dealing with such a problem exponential decay of the discrete state is commonly assumed with the decay rate determin...

RNDr. Přemysl Kolorenč, Ph.D.

Ústav teoretické fyziky (116. • 32-UTF)

2017

Petr Lukeš

Wave-packet basis in the description of the resonance scattering

Numerical evaluation of phase shifts in the quantum scattering theory relies on the good representation of continuum. Recently, novel approach to its discretization has been proposed, which is based on the so-called wave-packet basis. One of the advantages of this basis is perfect control over the density of the resulting discrete levels in various energy intervals. Student should study the usefulness of the basis for different numerical approaches to scattering problem.

Johannsen-Psaltis is a perturbation of the Kerr spacetime designed to avoid pathologies like naked singularities and closed time like curves. This spacetime depends not only on the mass and the spin of the central object, but also on extra parameters. In this thesis we consider only the lowest order extra parameter, and we show that the geodesic motion in this spacetime can exhibit chaotic behavior. We study the corresponding phase space by using Poincaré sections, rotation numbers and Lyapunov exponents.

The aim of this work is to analyze new vacuum solutions of Einstein’s gravitational field equations that allegedly represent accelerating (non-rotating) black holes with a NUT parameter. Although such solutions were mathematically found in 2006, their clear physical interpretation is still missing. The geometric and physical analysis will be based on explicit evaluation of the curvature scalars determining the algebraic type, finding suitable coordinates in which the acceleration can be set to zero, and elucidating the parameters related to the non-trivial NUT charge and acceleration.

prof. RNDr. Jiří Podolský, CSc., DSc.

Ústav teoretické fyziky (116. • 32-UTF)

2016

Jiří Trnka trnkajirka(at)seznam.cz

Semiclassical Monte-Carlo method in three particle scattering

Synthesis of molecules in the cosmic space is still not well understood. Conditions inside interstellar molecular clouds are so dramatically different from common laboratory conditions, that most of the processes that can take place there are not much explored. Quantum scattering theory describes such processes in principle exactly, but in practice the calculation is beyond computational power available even in the case of small molecules and we have to use clever approximations. A combination o...

doc. RNDr. Martin Čížek, Ph.D.

Ústav teoretické fyziky (116. • 32-UTF)

2016

Filip Vozáb

Particle interaction with atoms in optical lattice

Techniques of manipulation, trapping and cooling of atoms in optical laser field considerably developed during nineties. One of interesting applications is trapping of atoms in optical lattice, which is periodic potential formed by electromagnetic standing wave. Atoms in such lattice behave similarly like electrons or quasiparticles in solid state, but their properties could additionally be tuned with help of auxiliary electric or magnetic fields. Such configuration is a model system convenient ...

doc. RNDr. Martin Čížek, Ph.D.

Ústav teoretické fyziky (116. • 32-UTF)

2016

Dávid Matejov

Investigation of chaotic dynamical systems using the methods of Riemannian geometry

Causal sets represent one of the approaches to quantum gravity which from the beginning takes discrete structure of spacetime as given. To the set of discrete events are then added their causal relations. Dynamics of such a model might be given e.g. by sequential growth, where we add subsequent events and with certain probability generate their causal relations with original set.

RNDr. Otakar Svítek, Ph.D.

Ústav teoretické fyziky (116. • 32-UTF)

2015

Jan Dvořák

Elementary atomic collision processes in early Universe

Prediction of the relative abundance of the elements (H,D,He,Li) in the early Universe was one of the important arguments for the validity of the big bang theory. This prediction was based on models of nuclear reactions in hot dense plasma. Similar calculations are done also for later stages of universe, when the mater cooled significantly, so that atoms and molecules can form. Cross section for tens of reactions [2] are needed for such models. Goal of this work is critical revision of quality of these calculations (some of them are quite old). Calculation of selected reactions can be repeated or improved. Search of overlooked missing reactions can be attempted.

The aim of the bachelor thesis is to attempt to replace the singularity of a particular cylindrically symmetric solution of Einstein-Maxwell equations with a surface source and based on its properties, give a physical interpretation of the spacetime.

RNDr. Martin Žofka, Ph.D.

Ústav teoretické fyziky (116. • 32-UTF)

2015

Name

bachelor thesis

supervisor

department

graduated

Aleš Flandera

Higher spin theories in three dimensions

The aim of this project is to understand the theory of gravity coupled to massless higher spin fields in three spacetime dimensions. This theory can be formulated as a Chern-Simons theory and has a rich symmetry structure. The project will investigate these symmetries as well as the physical properties of conical defect solutions in the theory.

dr. Joris Raeymaekers

Ústav teoretické fyziky (116. • 32-UTF)

2014

Jiří Táborský

Multimode vibrational dynamics of electron scattering from molecule

Theoretical description of electron-molecule collisions still represents a great challenge. In addition to involving many particles, this theory is complicated by contribution of electron continuum and breakage of the Born-Oppenheimer approximation. All this problems are properly solved in the nonlocal resonance model theory [1,2]. This theory is used only for diatomic molecules. On the other hand, the equations of the nonlocal resonance model theory can easily be formulated for harmonic vibrati...

doc. RNDr. Martin Čížek, Ph.D.

Ústav teoretické fyziky (116. • 32-UTF)

2014

Matěj Hudec

Difraction of particle on slit with internal structure

Numerically exactly solvable problem of particle diffraction from structured barrier and its interpretation using approximate methods of solution. Student learns the key concepts of multichannel quantum scattering theory and resonances. This experience may serve as a basis for further work in atomic and molecular physics, particle physics or theory of electron transport in solid state.

Integral equations of scattering theory (Fredholm integral equations of the second kind) can be solved analytically for so-called separable interactions. It is the goal of this work to find such solutions for systems electron-atom or electron-molecule and to carry out their analytical continuation into the complex energy plane.

Analysis of the Stieltjes imaging method for the calculation of resonance widths

Calculation of resonance widths or decay rates of metastable states of atoms, molecules, and their ions represents very difficult problem for many-body quantum physics. The difficulty stems from the necessity of description of the electrons released to continuum. In practice, the continuum wave functions are often approximated using square-integrable functions that are widely used to describe bound states but cannot represent the scattered electron. However, the resulting pseudo-spectrum can sti...

RNDr. Přemysl Kolorenč, Ph.D.

Ústav teoretické fyziky (116. • 32-UTF)

2014

Bc. Jakub Kocák

Study of resonance and threshold effects on simple two-channel model

Analytically solvable model for two-channel scattering and its discussion in connection to theory of inelastic collisions in atomic and molecular physics. Student learns the key concepts of multichannel quantum scattering theory and resonances. This experience may serve as a basis for further work in atomic and molecular physics, particle physics or theory of electron transport in solid state.

The aim of this work is to demonstrate the best way in which dynamical electromagnetic and gravitational fields are represented in the Newtonian physics formalism, i.e., by using of the concept of force acting instantaneously at a distance. In particular, absence of the so called aberration will be explained. As a suitable explicit model, the Kinnersley class of exact solutions of Einstein’s equations which describe the field of arbitrarily accelerated sources will be used, including a possible cosmological constant.

The aim of the work is to summarize, compare, and further investigate exact spacetimes of Einstein’s equations of gravitational field with a null matter field that model an accelerated motion of localized objects – photon rockets. In particular, geometric and physical analysis of the Kinnersley and Bonnor classes of such spacetimes will be presented.

prof. RNDr. Jiří Podolský, CSc., DSc.

Ústav teoretické fyziky (32-UTF)

2012

Tibor Schmidt

Modeling the Mach's principle in the post-Minkowskian approximation to general relativity

When a distant quasar is gravitationally lensed by an intervening galaxy, several observable images of the quasar are formed by the gravitational field of the galaxy. In case the light of any of the images passes directly through the stellar population of the lensing galaxy, it is additionally influenced by all stars lying along its path. Taking into account the non-negligible angular motion of the quasar with respect to the caustic structure formed by the gravitational field of these stars, it ...

The motion of mass points in a gravitational field can be described and calculated rather easily. However, in the case of bodies with internal degrees of freedom, the situation is substantially more involved. Two mass points connected by a massless strut the length of which changes in time can modify the parameters of their orbit even in the Newtonian gravitational field. There are also examples of simple, extended objects that modify their orbit as they move on curved surfaces. This suggests a ...

Study of extremely narrow resonances in potential scattering. Development of numerical methods for very narrow resonances, or resonances with very different time scales for decay in two different channels.

The influence of the thermal emission of radiation from the surfaces
of asteroids and meteoroids on their orbital and rotational motion
is a frequently discussed application of the heat diffusion equation.
We call secular changes of the semimajor axis and the spin the
Yarkovsky/YORP effect. The existence of asteroids on unstable orbits,
structure of asteroid families or transport of meteoroids towards
the Earth is explained using the thermal effects.
Student should perform the following tasks: ...

Mgr. Miroslav Brož, Ph.D.

Astronomický ústav UK (32-AUUK)

2011

Name

bachelor thesis

supervisor

department

graduated

Tomáš Tintěra

Physical effect in anti-de Sitter and de Sitter universe

doc. RNDr. Pavel Krtouš, Ph.D.

UTF

2010

Pavel Brožek

Analytic continuation in coupling constant

The goal of this project is to study analytic properties of bound state energies and resonance parameters by means of simple potentials (sum of Dirac delta functions). It is in principle possible to determine resonance parameters from the knowledge of bound state energies by analytic continuation in the coupling constants. It is assumed that the analytic continuation will be carried out by the statistical Padé approximation (type III Padé).

prof. RNDr. Jiří Horáček, DrSc.

2010

Pavel Motloch

Relativistic tight-binding band-structure calculation of a multilayer

Spintronics is a field in microelectronics which utilizes both the electron charge and magnetic moment (spin). The orbital motion of the charge and the spin interact vie the magnetic exchange interaction or via the relativistic spin-orbit coupling. The thesis is motivated by a new direction in the spintronic research which studies these phenomena at interfaces of a ferromagnetic metal (e.g. Fe) and a non-magnetic semiconducor (Ga,As) or a ferromagnetic semiconductor (GaMnAs). The aim is basic mi...

Mgr. Tomáš Jungwirth, Dr.

UTF

2010

Martin Formánek formma(at)tiscali.cz

Time-dependent calculations in quantum mechanics

Summery of numerical methods for solving the time-dependent Schrödinger equation and comparison of their efficiency on simple one- and two-dimensional problems.

RNDr. Karel Houfek, Ph.D.

UTF

2010

Marek Bernát #marek.bernat(at)gmail.com

Potts antiferromagnet

prof. RNDr. Roman Kotecký, DrSc.

UTF

2010

Milan Šrámek #Kemrash(at)seznam.cz

Quaternions in physics

doc. RNDr. Jiří Langer, CSc.

2010

Petr Ducháček #duchy(at)seznam.cz

Timeless dynamics

When attempting to join quantum theory and general theory of relativity (while retaining covariance) it was realized that differing nature of time in these theories presents a nontrivial obstacle to their fusion. In general relativity, hamiltonian is a constraint and thus vanishes on physical solutions. Since hamiltonian generates the time evolution (both classical and quantum), it raised a question whether time is a truly fundamental and necessary quantity.

RNDr. Otakar Svítek, Ph.D.

UTF

2010

Anton Khirnov anton(at)khirnov.net

Falling into a black hole

Mgr. Tomáš Ledvinka, Ph.D.

UTF

2010

Name

bachelor thesis

supervisor

department

graduated

Michal Garlík

Topology in the Theory of Relativity

RNDr. Otakar Svítek, Ph.D.

UTF

2009

Peter Greškovič

Light scattering on a moving black hole

Mgr. Jiří Horák, Ph.D.

UTF/AUAV

2009

Eliška Lehečková #eliska.leheckova(at)gmail.com

Cosmological models and their perturbations

The work will summarize the basic models of the universe based both on the Newtonian theory of gravity and, above all, on the Einstein equations of general relativity. Linear perturbations of these models will be analyzed and the role of various gauges (i.e., of suitable coordinates) for solving specific physical situations like a condensation of a spherical mass or rotational effects, possibly also gravitational waves, will be investigated. At present nonlinear perturbations of the second order are started to be studied; in future, it would be interesting to touch upon this mathematically very complicated topic as well.

prof. RNDr. Jiří Bičák, DrSc., dr. h. c.

UTF

2009

Adam Přenosil

Newtonian Slip to Infinity in Finite Time

Survey of classical systems showing non-collision singularities in the solution of equations of motion.

Brownian motors are extremely interesting gadgets of nanometer size. We find them in living organisms, where they are responsible for intramolecular movements (we speak of molecular motors in this context), we can produce them artificially and use them in diverse nano-technologies. The theory of Brownian motors involves many open questions. One of them is the influence of mutual interaction of motors on their efficiency, both in the sense of particle current and energy. The student is expected to perform computations of the properties of simple schematic model of a Brownian motor and show the effect of interactions. They will be taken into account using an approximation of mean-field type.

RNDr. František Slanina, CSc.

UTF/FZU AV

2009

Daniel Perniš

Scattering theory in chains with tight-binding interaction and application on nanoelectromagnets

Theoretical description of the current conduction through metal-molecule-metal junction in the tight binding model and the formulation of the problem within quantum scattering theory.

In this work we study dynamics of systems in which their mass can change. We start from general Newton's law of motion, and in equations of motion we consider momentum change connected with the change of mass. In the first part of work we formulate and solve equations of motion for different examples of such systems. Examples are divided into three groups. The first group include Buquoys' problems where the mass is a function of coordinates. The second group includes conveyor-belt problems where...

The aim of this work is to study relations between some families of exact solutions of Einstein's gravitational field equations, in particular the conformally flat spacetimes with pure radiation (or analogous solutions of the algebraic type N) and a cosmological constant. Specifically, we present explicit transformations between the metric forms which have been recently found by Edgar and Ramos and solutions of this type found by Ozsváth, Robinson and Rózga that are known since 1980's.

In this work we study geometric formulation of Hamiltonian mechanics. At the beginning we look at situation, when the Hamiltonian function is time-independent. In this case our geometric arena is the n-dimensional symplectic manifold. After that we suppose time-dependent Hamiltonian function and we use 2n+1 dimensional extended phase space. Evolution of the mechanical system is given by integral curves of the vector field, which is determined by Hamilton's canonical equations. We also construct canonical transformations in both cases. In the end of this work we show geometric interpretation of the Hamiton-Jacobi equation.

In the present work we study application of differential geometry to the Lagrangian formalism. In the first chapter we summarize the foundations of geometric formulation of Lagrangian mechanics, in particular we show the principal meaning of the tagent bundle of the configuration manifold and dynamical vector field which solves the Lagrange equations in their geometrical form. The Noether's theorem is also formulated and proved. The second chapter introduces other geometrical definitions related...

doc. RNDr. Jiří Podolský, CSc., DSc.

ÚTF

2006

Jiří Lipovský JLipovsky(at)seznam.cz

Resonances in quantum graphs

Prof. RNDr. Pavel Exner, DrSc.

UJFAV

2006

Martin Váňa

Perturbations of bound states in broken waveguides

Prof. RNDr. Pavel Exner, DrSc.

UJFAV

2006

Pavel Čížek ciz(at)matfyz.cz

Weyl spacetimes with non-zero cosmological constant

doc. RNDr. Oldřich Semerák, Dr.

ÚTF

2006

David Vrba

"Spin-spin" interaction and the question of a binary-system stationary equilibrium in general